Journal of Applied and Industrial Mathematics最新文献

The algorithms for reconstructing a vector field from its known longitudinal or transverseray transforms of its moment are proposed and justified. The properties of several algorithms arestudied depending on the degree of data discretization, the level and type of noise introduced intothe data, the smoothness of the vector field, and the degree of connectivity of its support.Numerical simulations show good results of reconstructing vector fields from their momentum raytransforms.

Warehouses of the first echelon in a two-echelon system are designed to satisfy customerorders. In the second echelon, we have a central warehouse for restocking the first-echelonwarehouses. Customer orders can be partially satisfied, but the total fraction of completed ordersshould not be less than the specified threshold. We need to minimize the total cost of storing theitems in all warehouses. We use a deterministic simulation to calculate the order satisfaction ratioand the storage cost during the planning period. The simulation depends on inventorymanagement policies at each warehouse for each type of items. We develop a decompositionmethod for solving the problem. It is based on solution of subproblems for each type of items.Also, we propose some approaches to exact solution of the problem. The results of numericalexperiments with instances with 100 warehouses and 1000 types of items are presented. Oninstances with known exact solutions, we have the optimum in two cases, while in the other casesthe deviation from the optimal values is at most 1.9%.

We consider a dynamic competitive facility location problem modeling an interaction oftwo competing parties (Leader and Follower) who place their facilities within a planning horizonsplit into several time periods. The Leader is assumed to open his/her facilities at the beginningof the planning horizon and does not change his/her decision later, while the Follower can modifyhis/her choice within each time period. We propose an algorithm that computes the best Leader’sdecision and is built on the base of the branch-and-bound computational scheme. To computeupper bounds, a special relaxation of the initial bilevel problem strengthened with additionalconstraints (cuts) is used. The paper describes the construction of these constraints while utilizingauxiliary optimization problems; this provides the strongest cuts. On an instance of a dynamiccompetitive facility location on a network with three vertices, we demonstrate that the model iscapable to take into account information regarding the changes of problem’s parameters alongthe time period. An implementation of the branch-and-bound algorithm shows a significantbenefit from using the cuts specially designed for dynamic competitive models: it improves theupper bound’s quality and reduces the number of nodes in the branching tree.

A three-dimensional model of a blocky medium with elastic blocks and thin elastic andviscoelastic interlayers is considered. The interlayers are described by simplifieddifferential-difference relations. A numerical algorithm for solving dynamical problems based onsplitting method is presented. The results of simulation of wave propagation in blocky half-spaceare presented. We compare the behaviour of surface waves arising in a blocky layered medium andin a discrete periodic medium consisting of rigid masses connected to each other by elastic springs.Results of computations using the proposed model are in good agreement with the experimentaldata.

The aim of this work is to analyze the effect of the anisotropic nature of the electricconductivity in an oil-bearing formation on the induction logging signal. The numerical modelingof the logging signal from a device consisting of an alternating current excitation coil and tworeceiving coils moved along the wellbore is carried out. The electromotive force induced in thereceiving coils is investigated. The electric conductivity of the oil-bearing formation ischaracterized by either a diagonal tensor with dominant( sigma _{xx} ),( sigma _{yy} ) components or a dense tensor obtained by rotation to a specified zenithangle. Numerical modeling is performed with the vector finite element method on an adaptiveunstructured tetrahedral grid taking into account the geometry of the logging device, vertical well,and layered host medium. The tensor electric conductivity is plugged into the variationalformulation. Dependences of the apparent electric conductivity of the depth are obtained based onthe electromotive force induced in the receiving coils.

An increase in the concentration of carbon dioxide in the atmosphere caused by thecombustion of fuels has a negative impact on the current biosphere of the Earth. One way to getrid of excess carbon dioxide in the atmosphere is to capture and store it. Various methods forlong-term storage of carbon dioxide are proposed, including in various geological formations in gashydrate form, since gas hydrates have a number of unique properties, for example, it is possible tostably store a sufficiently large amount of gas in a small volume at a relatively low pressure. Oneof the objects for creating underground carbon dioxide storage facilities are depleted natural gasdeposits, since they are well studied, the characteristics of the deposits, their geometric dimensionsare known, and there are drilled wells. To study the patterns of the formation process of anunderground gas hydrate carbon dioxide storage, the article presents a mathematical model of theprocess of carbon dioxide injection into a zonally heterogeneous porous reservoir, initiallysaturated with methane and water, accompanied by the formation of gas hydrate. Unlike previousworks, the mathematical model additionally takes into account a number of factors: the solubilityof carbon dioxide in water, zonal heterogeneity of a reservoir, heat exchange of the reservoir withthe surrounding rocks impermeable to matter, filtration of water and gas. Numerical solutions ofthe problem were constructed to describe the distribution of parameters (pressure, temperature,carbon dioxide hydrate saturation) in the reservoir.

A mathematical model of raw materials processing is proposed. The production consists ofunits processing raw materials, storage tanks, and mixing units. The processing units are assumedto operate in one of two known modes. Switching from one mode to another can be carried out nomore than once. The problem of finding the optimal capacity of production at each of units, aswell as the time of switching units from one operating mode to another is formulated in a form ofdiscrete optimization problem. The solution of this problem should ensure an achievement of thespecified production plan. A method for its solution is proposed, including a transition toa convex statement, as well as an algorithm for discretizing the obtained control.

A difference system of the Lotka–Volterra type is considered. It is assumed that thissystem can operate both in some program and perturbed modes. The restrictions on the time ofthe system’s stay in these modes, providing the desired dynamical behavior, are investigated. Inparticular, the conditions of the ultimate boundedness of solutions and the permanence of thesystem are obtained. The direct Lyapunov method is used, and different Lyapunov functions areconstructed in different parts of the state space. The sizes of the domain of permissible initialvalues of solutions and the domain of the ultimate bound of solutions corresponding to therequired dynamics of the system are estimated. Constraints are set on the size of the digitizationstep of the system.

We consider the problem of minimizing the weighted average execution time ofequal-length jobs performance on one machine at the specified time of job arrival and thepossibility of their interruption. The computational complexity of this problem is currentlyunknown. The article proposes an algorithm for preprocessing input data that allows reducing theproblem to a narrower and more regular class of examples. The properties of optimal solutions aresubstantiated. Based on them, an algorithm for constructing a finite subset of solutions containingan optimal schedule has been developed. A parametric analysis of the schedules in this subset hasbeen carried out that makes it possible to form a subclass of schedules that are optimal at somevalues of weights. A polynomially solvable case of the problem is isolated.

This paper proposes a new approach to improving image quality in pulsed X-raytomography. The method is based on establishing a functional dependence of the reconstructedimages on the duration of the probing pulses and applying an extrapolation procedure. Thenumerical experiments demonstrated that the developed algorithm effectively suppresses theinfluence of scattered radiation and significantly increases image contrast. The proposedalternative approach allows substantially increasing the stability of the method even for mediacontaining strong scattering inhomogeneities and with a significant level of noise in the projectiondata. In addition, the algorithm has greater stability to errors in the source data caused by anincrease in the duration of the probing pulses. The numerical experiments confirmed the highefficiency of the extrapolation tomography algorithm for recovering the internal structure of thetest object.